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Local density approximation (LDA) to the density functional theory (DFT) hascontinuous derivative of total energy as a number of electrons function andcontinuous exchange-correlation potential, while in exact DFT both should bediscontinuous as number of electrons goes through an integer value. We proposeorbital densities functional (ODF) (with orbitals defined as Wannier functions)that by construction obeys this discontinuity condition. By its variationone-electron equations are obtained with potential in the form of projectionoperator. The operator increases a separation between occupied and empty bandsthus curing LDA deficiency of energy gap value systematic underestimation.Orbital densities functional minimization gives ground state orbital and totalelectron densities. The ODF expression for the energy of orbital densitiesfluctuations around the ground state values defines ODF fluctuation Hamiltonianthat allows to treat correlation effects. Dynamical mean-field theory (DMFT)was used to solve this Hamiltonian with quantum Monte Carlo (QMC) method foreffective impurity problem. We have applied ODF method to the problem ofmetal-insulator transition in lanthanum trihydride LaH_{3-x}. In LDAcalculations ground state of this material is metallic for all values ofhydrogen nonstoichiometry x while experimentally the system is insulating for x< 0.3. ODF method gave paramagnetic insulator solution for LaH_3 and LaH_{2.75}but metallic state for LaH_{2.5}.Comment: 35 pages, 5 figure

Orbital density functional as a means to restore the discontinuities in the total-energy derivative and the exchange–correlation potential